00:01
Hello.
00:03
So here we have an inductor capacitance circuit.
00:09
Okay, so the period of this circuit is just 2 pi i, 2 pi square root of the inductance times the capacitance.
00:23
So we have 2 pi.
00:26
The inductance is uh, let's see what i did, that's 8 millie henries so that's 8 times 10 to the negative 3 the capacitance is 10 micro fared so that's 10 times 10 to the negative 6 oh so if you crank this out you're going to get 1 .78 times 10 to the negative 3 seconds that is going to be the period of oscillation of the current.
01:23
First we call the second part.
01:24
So this is a, where we can b, we'll find the maximum current through the inductor.
01:38
So at imax the energy in the capacitance, or the capacitor equals the energy and the inductor.
01:51
And that's what we need to know for this, to be able to solve this part of the question.
01:56
Or we can also see that the energy in the capacitance is being transferred to the inductive.
02:02
So what is the formula for the charge? i'm sorry, the energy in the capacitor thus q squared over two times the capacitance equals energy stored in an inductor is half l i squared so here our distance or current is max.
02:32
So now if you isolate i max so these two can cancel that too.
02:38
So let's say i .mx squared is going to be equal to q squared over let's see.
02:54
So we have q squared over c, cl, yeah? so we can say imacs and then we go to q square root of 1 over cl or lc.
03:13
Okay, so what is the charge? so the charge is 60 microcule so that's going to be 60 times 10 to the minus 6 square root of 1 divided by the capacitance.
03:38
Let's see what the capacitance is.
03:45
That's 10, still 10, yeah? so we have 10 times 10 to the negative 6, that's 10 microphrates, right? let me just double chip, okay.
04:01
Then our inductance is still 8 millimetre.
04:07
That's 8 times 10 to the most is a second.
04:13
8 times 10 to the minus 3.
04:20
So if you crank this out, your maximum current is going to be 0 .212 ampers.
04:36
Then the third part of the question, let's see what that is.
04:40
So looking for the first time at which the energy is equally shared by the capacitance and the inductor.
04:48
Okay, so at a time t the charge on the capacitor is given by so we have kill equals kill none of the maximum charge cosine omega t and then when the time the energy is installed in the capacitor so if you want to transform this to energy okay because this one is just the charge on the capacitor.
05:32
Now the energy in this form is going to be q squared over 2c.
05:38
You remember that the, where is it? the energy stored in the capacitor is given by that, right? so we're just trying to write this in that form.
05:51
So we're going to have that equals, so this q not squared, 2l squared, omega, t, also divided by 2c.
06:04
Okay, so now we are trying to find the energy at time t when the energy is equally shared by the inductor in the capacitor.
06:20
So at that time, so it means that we are going to have half of the energy of the capacitors, right? so what can we do with that? we can say q not.
06:37
So this was not is the maximum, right? 2c let's see go squared omega oops i made a mistake here this is not squared uh t okay it's going to be equal to half oops it's a second of q squared over 2c so like i said the capacitor is going to have half of its maximum charge at this time when the energy is being shared.
07:20
And this is the exact expression we're going to use for that.
07:29
So at this point we just need to do some algebra and see what we can do here.
07:37
This guy can cancel this.
07:41
These two can cancel this two.
07:46
I can have close squared or make a t.
07:51
Oh yeah, this c can also cancel this c.
07:54
We will have just half.
07:56
Okay so this is close squared okay so of course we can find cause omega t is going to be square root of half okay now so cosine omega t let's see what that is so root of 0 .5 or that's going to be 0 .707 so omega t will be the cost inverse of 0 .707...